Simplify a combination

  • Thread starter Aleoa
  • Start date
  • #1
128
5
Member has been warned not to delete the template.
I'm trying to simplify the combination defined as : [itex]\binom{n}{\frac{n}{2}}[/itex].

I did some calculations, starting from the factorial formula [itex]\frac{n!}{(\frac{n}{2})!(\frac{n}{2})!}[/itex] and i found this form :

[itex]2^{n}(1-\frac{1}{n})(1-\frac{1}{n-2})(1-\frac{1}{n-4})...[/itex]

but i don't know how to continue, can you help me ?
 

Answers and Replies

  • #2
fresh_42
Mentor
Insights Author
2021 Award
16,427
15,469
but i don't know how to continue, can you help me ?
No, since you haven't said what your goal is. To me ##\binom{n}{\frac{n}{2}}## is already fine.
 
  • #3
128
5
I want to characterize the behaviour of the formula as n become larger, so i'm trying to simplify it . I'm sorry for the template, next time i'll write it correctly. Thanks for the support
 
  • #4
fresh_42
Mentor
Insights Author
2021 Award
16,427
15,469
I want to characterize the behaviour of the formula as n become larger, so i'm trying to simplify it . I'm sorry for the template, next time i'll write it correctly. Thanks for the support
In this case I'd try where Stirling's approximation would get me.
 
  • #5
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722
I want to characterize the behaviour of the formula as n become larger, so i'm trying to simplify it . I'm sorry for the template, next time i'll write it correctly. Thanks for the support

As fresh_42 suggested, use Stirling's formula. Every student of probability should be thoroughly familiar with that formula, as it is used everywhere.
 

Related Threads on Simplify a combination

  • Last Post
Replies
4
Views
975
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
16
Views
786
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
15
Views
2K
  • Last Post
Replies
1
Views
2K
Top